Two cents here and not at all a commentary on your handling of your kids, just in relation to the topic; my therapist told me that she perceives "compensating" as causing the most damage to kids coping with having an incompetent parent (that's my choice of words). Having thought a lot about it and extrapolating as I love to do, I think trying to fill that void of other parent when other parent is alive and has the option (if not ability) of being a decent parent, damages in a very roundabout way and really shifts a burden of responsibility onto the "present" and "better" parent. Your child's assertion that you are a better mommy than mommy MIGHT (not "is" cuz I don't know) be an indication that you are overcompensating...you are dad, not mom. I definitely don't want to argue this as I think you're awesome and I am not familiar enough to make any assessment. I am relating. My kids' dad is physically gone much of the time. I am trying to come to terms with the fact that I cannot be their father. They have a dad whom they are connected to and his absence is part of their relationship and in some way part of the wholeness of that relationship, I can't fill that void. I am looking to involve other men (not lovers LOL, but grandfather, family friends) to contribute positive male relationships and modeling.
You're a smarter than average guy, search your soul. When you make peace with the fact that that IS their mother, limitations and all, and there is no amount of compensating that will change or fix that, you'll suffer less.
The torture as I relate to it is (as you've pointed out), seeing your kids suffer. It takes a degree of stoicism I have yet to attain to absorb their pain without suffering myself. But it is getting better.
Oh, one other haunting frustration is knowing that the crappy parent (yes I said it) is modeling for the kids. That sucks and I finally realize that it is BS that I will make up for that somehow. I'm letting myself off the hook for that. I model the mommy part and he models the daddy part and that's that. It sucks but it is a relief to take that heat off of myself. It is trite and it makes people feel better to tell me how I will somehow compensate for that but it is such a set up. The best modeling I can do is as a woman and mother.
I know that my H's mother described herself as being the mother and father to her children (though they had a living father who was just a jerk and often absent). Well, it bit her in the ass because they hold her responsible and have little appreciation for what she went through...she modeled somehow that it was her duty to fill both rolls and it let him off the hook. I don't know if that makes sense or if any of this does. I hope so.